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Summary
This summary is machine-generated.

This study introduces a new inequality connecting system response and fluctuations in steady states. It provides a universal bound for signal-to-noise ratio in noisy dynamics, applicable across various physical systems.

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Area of Science:

  • Statistical physics
  • Non-equilibrium thermodynamics
  • Physical systems analysis

Background:

  • Understanding the relationship between system dynamics and fluctuations is crucial in statistical physics.
  • Existing theories often focus on equilibrium conditions or specific types of dynamics.

Purpose of the Study:

  • To derive a general inequality linking finite-frequency linear response and fluctuations in steady-state systems.
  • To establish a universal upper bound for the broadband signal-to-noise ratio in noisy dynamics.
  • To explore conditions under which this inequality becomes an equality.

Main Methods:

  • Derivation of a novel inequality for general Markovian dynamics.
  • Analysis of both overdamped and underdamped Langevin systems and jump processes.
  • Investigation of systems both in and out of thermodynamic equilibrium.

Main Results:

  • A universal inequality relating linear response and fluctuations is established.
  • A universal upper bound on the broadband signal-to-noise ratio is derived, dependent only on damping and temperature.
  • Conditions for the inequality to become an equality in linear systems are identified.

Conclusions:

  • The derived inequality offers a fundamental connection between response and fluctuations applicable to a wide range of physical systems.
  • The universal bound on signal-to-noise ratio has implications for designing and analyzing noisy systems.
  • The findings extend the understanding of fluctuation-dissipation relations beyond equilibrium conditions.